An unconditionally convergent finite-difference scheme for the SIR model

摘要

A first-order, unconditionally-stable, finite-difference scheme is developed for the numerical solution of the SIR model. It is seen that numerical simulations using the method reflect the long-term behaviour of the continuous-time system accurately. The introduction of seasonal variation into the SIR model leads to periodic and chaotic dynamics of epidemics which are present in the numerical simulations.